The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+X  1  1 X^2+2  1  1  2  1  1  1 X^2  1 X+2  1  1  1  1  1  1  1  1 X^2+2 X^2+2  0
 0  1 X+1 X^2+X X^2+1  1 X^2+X+2 X^2+X+1  1  X X+1  1 X^2+2  3  1  2 X^2+3  1 X+2 X^2 X^2+X+3  1  1  1  0  0 X^2+X+2 X^2+X+2 X^2+X+2  2 X^2+X+1  1  1  1  X
 0  0 X^2  0  2 X^2+2 X^2+2 X^2+2 X^2 X^2  2  0  0  2  0 X^2 X^2+2 X^2  2 X^2  0 X^2 X^2+2  2  0  2 X^2 X^2+2  0  2 X^2+2 X^2  2  0  0
 0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0

generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+281x^32+192x^33+356x^34+384x^35+392x^36+192x^37+216x^38+28x^40+4x^42+2x^48

The gray image is a code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 0.063 seconds.